Here is an MSDN article with lots of links to other articles relating to SQL Server Security.
Here is an article that talks about restricting interactive login for SQL Analysis services
Depending on what the DBA's job responsibilities include and what you mean by "SQL Server", the DBA might need administrator rights. SQL Server could mean SQL Database Engine or Analysis Services or Integration Services or Reporting Services.
And then there is backups and restores and where those files sit. Does the DBA need to create new databases and can he/she create the data files and log files for those without admin rights. What about restarting services?
No the DBA does not have to be an administrator of the machine, but often the DBA is expected to do a lot of tasks that require those permissions.